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Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  1.0 & -7.00 x_{1} & -10.00 x_{2} & -6.00 x_{3} & -1.00 x_{4} & -3.00 x_{5} & +  8.00 x_{6} & -10.00 x_{7} & +  6.00 x_{8} & -8.00 x_{9}\\
 x_{11}   &  -3.0 & -1.00 x_{1} &   & +  9.00 x_{3} & +  2.00 x_{4} & +  1.00 x_{5} & -5.00 x_{6} & +  5.00 x_{7} & -6.00 x_{8} & +  1.00 x_{9}\\
 x_{12}   &  0.0 & -9.00 x_{1} & -2.00 x_{2} & +  1.00 x_{3} & -4.00 x_{4} & -2.00 x_{5} & -4.00 x_{6} & -4.00 x_{7} & -10.00 x_{8} & -2.00 x_{9}\\
 x_{13}   &  -3.0 & -10.00 x_{1} & -4.00 x_{2} & +  9.00 x_{3} & +  5.00 x_{4} & +  2.00 x_{5} & -2.00 x_{6} & +  5.00 x_{7} & -5.00 x_{8} & +  8.00 x_{9}\\
 x_{14}   &  0.0 & -4.00 x_{1} & -5.00 x_{2} & -2.00 x_{3} & -4.00 x_{4} & -8.00 x_{5} & -3.00 x_{6} & +  2.00 x_{7} & +  4.00 x_{8} & +  4.00 x_{9}\\
\hline
z    &  0.0 & +  2.00 x_{1} & +  4.00 x_{2} & -3.00 x_{3} & +  3.00 x_{4} & -1.00 x_{5} & +  3.00 x_{6} & +  1.00 x_{7} &   & +  4.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,14$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  7.00 y_{10} & +  1.00 y_{11} & +  9.00 y_{12} & + 10.00 y_{13} & +  4.00 y_{14}\\
 y_{2}   &  1.0 & + 10.00 y_{10} &   & +  2.00 y_{12} & +  4.00 y_{13} & +  5.00 y_{14}\\
 y_{3}   &  1.0 & +  6.00 y_{10} & -9.00 y_{11} & -1.00 y_{12} & -9.00 y_{13} & +  2.00 y_{14}\\
 y_{4}   &  1.0 & +  1.00 y_{10} & -2.00 y_{11} & +  4.00 y_{12} & -5.00 y_{13} & +  4.00 y_{14}\\
 y_{5}   &  1.0 & +  3.00 y_{10} & -1.00 y_{11} & +  2.00 y_{12} & -2.00 y_{13} & +  8.00 y_{14}\\
 y_{6}   &  1.0 & -8.00 y_{10} & +  5.00 y_{11} & +  4.00 y_{12} & +  2.00 y_{13} & +  3.00 y_{14}\\
 y_{7}   &  1.0 & + 10.00 y_{10} & -5.00 y_{11} & +  4.00 y_{12} & -5.00 y_{13} & -2.00 y_{14}\\
 y_{8}   &  1.0 & -6.00 y_{10} & +  6.00 y_{11} & + 10.00 y_{12} & +  5.00 y_{13} & -4.00 y_{14}\\
 y_{9}   &  1.0 & +  8.00 y_{10} & -1.00 y_{11} & +  2.00 y_{12} & -8.00 y_{13} & -4.00 y_{14}\\
\hline
z    &  -0 & -1.00 y_{10} & +  3.00 y_{11} &   & +  3.00 y_{13} &   \\
\end{array}\]
Unbounded Dictionary!
Initialization returns unbounded dual dictionary after 3 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  3.66666666667 & -1.64 y_{6} & -1.02 y_{3} & + 14.55 y_{12} & +  4.07 y_{13} & + 10.98 y_{14}\\
 y_{2}   &  4.33333333333 & -2.14 y_{6} & -1.19 y_{3} & +  9.38 y_{12} & -2.43 y_{13} & + 13.81 y_{14}\\
 y_{11}   &  0.333333333333 & -0.14 y_{6} & -0.19 y_{3} & +  0.38 y_{12} & -1.43 y_{13} & +  0.81 y_{14}\\
 y_{4}   &  0.666666666667 & +  0.07 y_{6} & +  0.26 y_{3} & +  3.98 y_{12} & -2.79 y_{13} & +  3.26 y_{14}\\
 y_{5}   &  1.66666666667 & -0.50 y_{6} & -0.17 y_{3} & +  3.83 y_{12} & -2.50 y_{13} & +  9.83 y_{14}\\
 y_{10}   &  0.333333333333 & -0.21 y_{6} & -0.12 y_{3} & +  0.74 y_{12} & -0.64 y_{13} & +  0.88 y_{14}\\
 y_{7}   &  2.66666666667 & -1.43 y_{6} & -0.24 y_{3} & +  9.48 y_{12} & -4.29 y_{13} & +  2.76 y_{14}\\
 y_{8}   &  1.0 & +  0.43 y_{6} & -0.43 y_{3} & +  7.86 y_{12} & +  0.29 y_{13} & -4.43 y_{14}\\
 y_{9}   &  3.33333333333 & -1.57 y_{6} & -0.76 y_{3} & +  7.52 y_{12} & -11.71 y_{13} & +  2.24 y_{14}\\
\hline
z    &  0.666666666667 & -0.21 y_{6} & -0.45 y_{3} & +  0.40 y_{12} & -0.64 y_{13} & +  1.55 y_{14}\\
\end{array}\]
Original Problem is Infeasible
Infeasible Problem.. Early Exit
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